Question

Jerome takes a math course and a science course for summer school. For every 5 hours Jerome spends studying math, he studies science for 4 hours. If Jerome spent a total of 54 hours studying last week, then how long did he study math?

Answer 1

`y= (54*4)/(9)=24`

And then we can solve for x like this:

`x = (5*24)/(4)=30`

And the final solution would be 30 hours for math and 24 for the science course.

Explanation:

We need to define some notation first. Let

x= number of hours that he spent for the math course

y = number of hours that he spent for th science course

We have that the total of hours is 54, and we can write that like this:

`x+ y = 54` (1)

And the other conditions is: " For every 5 hours Jerome spends studying math, he studies science for 4 hours" And we can write this like that:

`(x)/(y)=(5)/(4)`

And we can solve for x like this:

`x = (5y)/(4)`

And we can replace this into equation (1) and we got:

`(5y)/(4) + y = 54`

And if we do the algebra we got:

`(9y)/(4) =54`

`y= (54*4)/(9)=24`

And then we can solve for x like this:

`x = (5*24)/(4)=30`

And the final solution would be 30 hours for math and 24 for the science course.

Answer 2

Jerome spent
`30` hours studying mathematics

Explanation:

We were given that every 5 hours Jerome spends studying math. he studies science for 4 hours.

The ratio of Mathematics to Science is

`5:4` respectively.

The total ratio is
`5+4=9`.

If Jerome spent a total of
`54` hours studying last week, then the number of hours he spent studying mathematics is

`=(5)/(9)* 54`.

`=(5)/(1)* 6`.

`=30` hours.